"The number is the truth about my body"
The scale is honest. It doesn't flatter and it doesn't sulk. So the number feels like the truth, and the truth it feels like is a truth about fat, because fat is the thing you're worried about. But that's not what a scale measures. It measures the downward force of everything that's currently in you and on you, and from one morning to the next, the things that change most aren't fat.
Start with water. Kreitzman, Coxon and Szaz, writing in the American Journal of Clinical Nutrition in 1992, describe how the body's stored fuel, glycogen, is kept in the liver and muscles with three to four parts of water bound to it. Eat more carbohydrate than usual and you store more glycogen and more water with it, and the scale goes up by the weight of both. Eat less, or cut carbohydrate, and the store drains and the water goes with it, and the scale drops by a figure that looks like fat and is mostly a fuel tank emptying. Their paper is about very low calorie diets, but the mechanism is the same on an ordinary Tuesday.
Then salt. A salty meal holds water in the body until the kidneys have dealt with it, which takes a day or two. Then the contents of your gut, which on any morning include whatever hasn't left yet from the last day or so. Then the time of day, since you're lighter after the loo and before a drink, which is why you weigh when you do. Then clothes.
Then, for a lot of readers, the month. Spyridon Kanellakis and colleagues measured 42 women twice a week across one menstrual cycle and found weight about half a kilo higher during menstruation than in the first week, and the difference was almost exactly the rise in the water outside the cells. A much older and much smaller study, by Bunt, Lohman and Boileau, followed seven women who reported big swings across the month and measured them at their lightest and heaviest. The average gap was about two kilos, and that's a self-selected seven, so don't take it as typical. Take it as a sign of how wide the range can be.
None of these is fat. Add them up and you have the ordinary range of a body doing what bodies do between one morning and the next. Fat changes too, of course. It changes slowly, in amounts a bathroom scale can't pick out from the rest of the traffic on any one day. The number is true. It just isn't the truth you're reading it as.